Spectral properties of general hypergraphs

Abstract

In this paper, we investigate spectral properties of the adjacency tensor, Laplacian tensor and signless Laplacian tensor of general hypergraphs (including uniform and non-uniform hypergraphs). We give some properties for the spectral radius of hypergraphs, and obtain spectral upper bounds for the chromatic number of hypergraphs. The odd-bipartiteness of hypergraphs can be recognized from the spectrum. We give a relation between the analytic connectivity and edge connectivity of a hypergraph, and show that a hypergraph with even rank is connected if and only if its analytic connectivity is larger than 0. We also give some relations between the analytic bipartiteness and odd-bipartiteness of hypergraphs.